Applicability Limits of the Born Rule Under Identity Failure Probabilistic Descriptions at the Boundary of Quantum Persistence

The Born rule assigns probabilities to measurement outcomes under the assumption that a quantum system retains a well-defined identity within a stable coarse-grained description. Experimental studies of open quantum systems, error correction, monitored dynamics, and decoherence report abrupt “avalanche”-like transitions in which probabilistic descriptions of subsystems rapidly fail, even though global unitary evolution is preserved. This work provides a structural interpretation of such transitions by identifying an identity tolerance boundary, denoted Ω, beyond which the thermodynamic identity of a quantum system ceases to be well defined. When cumulative irreversible entanglement or decoherence exceeds this boundary, Born-rule probabilities no longer apply—not due to a failure of quantum mechanics, but because the probabilistic description presupposes a persisting system identity that has been lost. The framework does not introduce new physical laws, collapse mechanisms, or modifications to quantum theory. Rather, it clarifies the domain of applicability of probabilistic descriptions by explicitly separating fine-grained unitary evolution from the persistence of macroscopic or subsystem identity. This perspective unifies observations across decoherence avalanches, error-correction thresholds, and measurement-induced transitions without proposing operational procedures or control mechanisms.